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Analytic interpolation problems with rationality and derivative constraintsare ubiquitous in systems and control. This paper provides a new method forsuch problems, both in the scalar and matrix case, based on a non-standardRiccati-type equation. The rank of the solution matrix is the same as thedegree of the interpolant, thus providing a natural approach to modelreduction. A homotopy continuation method is presented and applied to someproblems in modeling and robust control. We also address a question on thepositive degree of a covariance sequence originally posed by Kalman.

The Covariance Extension Equation: A Riccati-type Approach to Analytic Interpolation